8.4.22 problem 22

Internal problem ID [725]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:59:16 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 16

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

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