83.40.4 problem 4

Internal problem ID [19476]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (E) at page 140
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:45:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 22

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

\[ y(x)\to x^2+x-c_2 x+c_1 e^x+1 \]