Question
Find the solution of the differential equation $\frac{d y}{d x}=x^3 e^{-2 y}$.
✓
Answer
$\int \frac{d y}{e^{-2 y}}=\int x^3 d x$
$\int e^{2 y} d y=\int x^3 d x$
or, $\frac{e^{2 y}}{2}=\frac{x^4}{4}+C$
or, $\frac{1}{2} e^{2 y}=\frac{x^4}{4}+C$
$2 e^{2 y}=x^4+C_1 \quad$ where $\left(C_1=4 C\right)$
$\int e^{2 y} d y=\int x^3 d x$
or, $\frac{e^{2 y}}{2}=\frac{x^4}{4}+C$
or, $\frac{1}{2} e^{2 y}=\frac{x^4}{4}+C$
$2 e^{2 y}=x^4+C_1 \quad$ where $\left(C_1=4 C\right)$
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