15.6.4 problem 4

Internal problem ID [2961]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:04:31 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \left (x^{3}+c_{1} \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 15

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

\[ y(x)\to e^x \left (x^3+c_1\right ) \]