Internal problem ID [10261]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear
equation. Page 114
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve((x+1)^2*diff(y(x),x$2)-(x+1)*diff(y(x),x)+6*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = \left (x +1\right ) \sin \left (\sqrt {5}\, \ln \left (x +1\right )\right ) c_{2}+\left (x +1\right ) \cos \left (\sqrt {5}\, \ln \left (x +1\right )\right ) c_{1}+\frac {x}{5}+\frac {1}{30} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 49
DSolve[(x+1)^2*y''[x]-(x+1)*y'[x]+6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{30} (6 x+1)+c_2 (x+1) \cos \left (\sqrt {5} \log (x+1)\right )+c_1 (x+1) \sin \left (\sqrt {5} \log (x+1)\right ) \\ \end{align*}