# arrow_back Show that the solution of the above differential equation is $$y=\frac{1}{2}\left(\mathrm{e}^{2 x}+3\right) \cos x .$$

104 views
$$\frac{d y}{d x}+y \tan x=\mathrm{e}^{2 x} \cos x, y(0)=2 \text {. }$$
Show that the solution of the above differential equation is
$$y=\frac{1}{2}\left(\mathrm{e}^{2 x}+3\right) \cos x .$$

## Related questions

close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
One possible integrating factor for the following linear differential equation is $X \frac{d Y}{d X}+(X+1) Y=3 X^{2} e^{-X}$
One possible integrating factor for the following linear differential equation is $X \frac{d Y}{d X}+(X+1) Y=3 X^{2} e^{-X}$ One possible integrating factor for the following linear differential equation is \ X \frac{d Y}{d X}+(X+1) Y=3 X^{2} e^{-X} \ &nbsp; ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Calculate the $\mathrm{y}$-intercept of $y=\left(\frac{1}{2}\right)^{x}$.
Calculate the $\mathrm{y}$-intercept of $y=\left(\frac{1}{2}\right)^{x}$.Calculate the $\mathrm{y}$-intercept of $y=\left(\dfrac{1}{2}\right)^{x}$. ...
Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$
Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$Evaluate $\lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)$ ...
Perform the indicated operations. Write each answer using only positive exponents. Assume all variables represent positive real numbers. $$\frac{9 m^{1 / 2} n^{3 / 2}}{m^{-7} n\left(m^{3} n\right)^{1 / 2}}$$Perform the indicated operations. Write each answer using only positive exponents. Assume all variables represent positive real numbers. $$\frac{9 m^ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right) 1 answer 109 views Evaluate \lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right)Evaluate \lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-2 x-3}{x^{2}-1}\right) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right )  1 answer 176 views Evaluate \lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right ) Evaluate \lim_{x \to \infty } \left ( \frac{2x^{2}-2x-3}{x^{2}-1} \right )  ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Simplify \left(\dfrac{2 x^{3}}{8 y^{-4}}\right)^{-3} 1 answer 92 views Simplify \left(\dfrac{2 x^{3}}{8 y^{-4}}\right)^{-3}Simplify \left(\dfrac{2 x^{3}}{8 y^{-4}}\right)^{-3} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$0 answers 119 views If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For integers n>1, show that$$ \left(\frac{1}{2}+\frac{2}{3}+\cdots+\frac{n}{n+1}\right)^{n}>\frac{n^{n}}{n+1} . $$1 answer 152 views For integers n>1, show that$$ \left(\frac{1}{2}+\frac{2}{3}+\cdots+\frac{n}{n+1}\right)^{n}>\frac{n^{n}}{n+1} . $$For integers n&gt;1, show that$$ \left(\frac{1}{2}+\frac{2}{3}+\cdots+\frac{n}{n+1}\right)^{n}&gt;\frac{n^{n}}{n+1} . $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let n>1 be an integer. Show that$$ n !<\left(\frac{n+1}{2}\right)^{n} $$1 answer 152 views Let n>1 be an integer. Show that$$ n !<\left(\frac{n+1}{2}\right)^{n} $$Let n&gt;1 be an integer. Show that$$ n !&lt;\left(\frac{n+1}{2}\right)^{n} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} . $$1 answer 120 views Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} . $$Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} . $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that {(2x-1)}^{2}-{(x-3)}^{2} can be simplified to (x+2)(3x-4). 1 answer 182 views Show that {(2x-1)}^{2}-{(x-3)}^{2} can be simplified to (x+2)(3x-4).Show that {(2x-1)}^{2}-{(x-3)}^{2} can be simplified to (x+2)(3x-4). ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For the function f(x)=-3 x+4, find and simplify$$ \frac{f(x+h)-f(x)}{h} $$1 answer 123 views For the function f(x)=-3 x+4, find and simplify$$ \frac{f(x+h)-f(x)}{h} $$For the function f(x)=-3 x+4, find and simplify$$ \frac{f(x+h)-f(x)}{h} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the given differential equation$$ y^{\prime}-y \tan (x)=8 \sin ^{3}(x) $$1 answer 72 views Solve the given differential equation$$ y^{\prime}-y \tan (x)=8 \sin ^{3}(x) $$Solve the given differential equation$$ y^{\prime}-y \tan (x)=8 \sin ^{3}(x)  ...