7.4.22 problem 22

Internal problem ID [94]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 22
Date solved : Friday, February 07, 2025 at 07:49:09 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

dsolve([diff(y(x),x)=2*x*y(x)+3*x^2*exp(x^2),y(0) = 5],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x^{2}} \left (x^{3}+5\right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 16

DSolve[{D[y[x],x]==2*x*y[x]+3*x^2*Exp[x^2],{y[0]==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2} \left (x^3+5\right ) \]