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Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]3 Marks
Question
Solve the following differential equation $\frac{ d y}{ d x}= x ^2 y + y$
✓

Answer

$ \frac{ d y}{ d x}= x ^2 y + y$
$=\left( x ^2+1\right) y$
$\therefore \frac{1}{y} d y=\left( x ^2+1\right) dx $
Integrating on both sides, we get
$ \int \frac{1}{y} d y=\int\left(x^2+1\right) d x$
$\therefore \log | y |=\frac{x^3}{3}+x+c $

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