Internal problem ID [11302]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y=\left (1-x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=(1-x)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x +c_{1} {\mathrm e}^{x}+x^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 22
DSolve[(1-x)*y''[x]+x*y'[x]-y[x]==(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+x-c_2 x+c_1 e^x+1 \]