Internal problem ID [5425]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+x \right ) y^{\prime \prime }-\left (4+3 x \right ) y^{\prime }+3 y=\left (3 x +2\right ) {\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((x+1)*diff(y(x),x$2)-(3*x+4)*diff(y(x),x)+3*y(x)=(3*x+2)*exp(3*x),y(x), singsol=all)
\[ y = \left (x +\frac {4}{3}\right ) c_{2} +c_{1} {\mathrm e}^{3 x}+x \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.364 (sec). Leaf size: 48
DSolve[(x+1)*y''[x]-(3*x+4)*y'[x]+3*y[x]==(3*x+2)*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} \left (x+\frac {2}{3}\right )+\frac {c_1 e^{3 x+3}}{\sqrt {2}}-\frac {1}{9} \sqrt {2} c_2 (3 x+4) \]