Question

The solution of $\frac{dy}{dx}=e^{3x-2y}+x^2{e}^{-2y}$

• A. $y=log(e^{3x}+x^2)+c$
• B. $y=2log(e^{3x}+x^2)+c$
• C. $2e^{2x}=3(e^{3y}+y^3)+c$
• D. $3e^{2y}=2(e^{3x}+x^3)+c$

Answer 1

The correct option is D $3e^{2y}=2(e^{3x}+x^3)+c$

$\frac{dy}{dx}=e^{-2y}(e^{3x}+x^2)$

$\Rightarrow \int e^{2y}dy=\int (e^{3x}+x^2)dx+c$

$\Rightarrow \frac{e^2}{2}=\frac{e^{3x}}{3}+{}^{x3}{/}_3+c$

$3e^{2y}=2(e^{3x}+x^3)+c$