30.4 problem Ex 4

Internal problem ID [10278]

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]]

Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y-\left (1-x \right )^{2}=0} \end {gather*}

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)
 

\[ y \relax (x ) = x c_{2}+c_{1} {\mathrm e}^{x}+x^{2}+1 \]

Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 22

DSolve[(1-x)*y''[x]+x*y'[x]-y[x]==(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2+x-c_2 x+c_1 e^x+1 \\ \end{align*}