15.15.6 problem 6

Internal problem ID [3210]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:26:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

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

\[ y = \frac {{\mathrm e}^{-2 x} \left (3 c_{1} {\mathrm e}^{\frac {5 x}{2}}+\left (x^{2}-\frac {14}{3} x +\frac {86}{9}\right ) {\mathrm e}^{3 x}+3 c_2 \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 41

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

\[ y(x)\to \frac {1}{27} e^x \left (9 x^2-42 x+86\right )+c_1 e^{x/2}+c_2 e^{-2 x} \]