Internal problem ID [5411]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre).
Supplemetary problems. Page 110
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (1+2 x \right )^{2} y^{\prime \prime }-2 \left (1+2 x \right ) y^{\prime }-12 y=6 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve((2*x+1)^2*diff(y(x),x$2)-2*(2*x+1)*diff(y(x),x)-12*y(x)=6*x,y(x), singsol=all)
\[ y = \frac {c_{1}}{2 x +1}+\left (2 x +1\right )^{3} c_{2} -\frac {24 x^{2}+8 x +1}{32 \left (2 x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 41
DSolve[(2*x+1)^2*y''[x]-2*(2*x+1)*y'[x]-12*y[x]==6*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-24 x^2-8 x+32 c_1 (2 x+1)^4-1+32 c_2}{32 (2 x+1)} \]