64.5.20 problem 20

Internal problem ID [13333]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 05:22:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

dsolve([diff(y(x),x)+3*x^2*y(x)=x^2,y(0) = 2],y(x), singsol=all)
 

\[ y = \frac {1}{3}+\frac {5 \,{\mathrm e}^{-x^{3}}}{3} \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 20

DSolve[{D[y[x],x]+3*x^2*y[x]==x^2,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 e^{-x^3}}{3}+\frac {1}{3} \]