40.13.6 problem 26

Internal problem ID [6760]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:27:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y&=\left (-x^{2}+6\right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)-x*(2*x+3)*diff(y(x),x)+(x^2+3*x+3)*y(x)=(6-x^2)*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_1 \,x^{3}+c_2 x +x^{2}+2\right ) \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 30

DSolve[x^2*D[y[x],{x,2}]-x*(2*x+3)*D[y[x],x]+(x^2+3*x+3)*y[x]==(6-x^2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^x \left (c_2 x^3+2 x^2+2 c_1 x+4\right ) \]