Internal problem ID [5415]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y=\left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = {\mathrm e}^{2 x} x +{\mathrm e}^{x} \left (c_{1} x^{2}+2 c_{1} x +c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 32
DSolve[(x+1)*y''[x]-(2*x+3)*y'[x]+(x+2)*y[x]==(x^2+2*x+1)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x \left (2 e^x x+e c_2 (x+2) x+2 e c_1\right ) \]