40.13.4 problem 24

Internal problem ID [6758]
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 : 24
Date solved : Monday, January 27, 2025 at 02:27:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y&=\left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

dsolve((x+1)*diff(y(x),x$2)-(2*x+3)*diff(y(x),x)+(x+2)*y(x)=(x^2+2*x+1)*exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 32

DSolve[(x+1)*D[y[x],{x,2}]-(2*x+3)*D[y[x],x]+(x+2)*y[x]==(x^2+2*x+1)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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