Internal problem ID [11275]
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]]
\[ \boxed {\left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y=x} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \left (1+x \right ) \sin \left (\sqrt {5}\, \ln \left (1+x \right )\right ) c_{2} +\left (1+x \right ) \cos \left (\sqrt {5}\, \ln \left (1+x \right )\right ) c_{1} +\frac {x}{5}+\frac {1}{30} \]
✓ Solution by Mathematica
Time used: 0.508 (sec). Leaf size: 49
DSolve[(x+1)^2*y''[x]-(x+1)*y'[x]+6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{30} (6 x+1)+c_2 (x+1) \cos \left (\sqrt {5} \log (x+1)\right )+c_1 (x+1) \sin \left (\sqrt {5} \log (x+1)\right ) \]