Question

Solve differential equationdy/dx= 15x^2 e^-y

First order differential equations
ANSWERED
asked 2020-11-05

Solve differential equation \(dy/dx= 15x^2 e^{-y}\)

Answers (1)

2020-11-06

\(dy/dx= 15x^2 e^{-y}\)
\(e^ydy= 15x^2dx\) (1)
On integrating equation (1) we get
\(\int e^{y}dy= 15 \int x^{2}dx\)
\(\Rightarrow e^{y}=5x^{3}+C\) (2)
Take logarithmic on the both side if equation (2) we get
\(\ln(e^y)= \ln(abs(5x^3+c))\)
\(\Rightarrow y \ln(e)=\ln(abs(5x^3+c))\)
\(\Rightarrow y= \ln(abs(5x^3+c))\)
\(y(x)=\ln(abs(5x^3+c))\)

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