Internal problem ID [10322]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62.
Summary. Page 144
Problem number: Ex 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve((x^2-x)*diff(y(x),x$2)+(4*x+2)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (12 x^{3} \ln \left (x \right )-3 x^{4}+18 x^{2}-6 x +1\right ) c_{1}}{\left (x -1\right )^{5}}+\frac {x^{3} c_{2}}{\left (x -1\right )^{5}} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 46
DSolve[(x^2-x)*y''[x]+(4*x+2)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-3 c_1 x^3-3 c_2 \left (x^3-6 x+2\right ) x+12 c_2 x^3 \log (x)+c_2}{3 (x-1)^5} \\ \end{align*}