83.40.8 problem 8

Internal problem ID [19480]
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 : 8
Date solved : Tuesday, January 28, 2025 at 01:46:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve(x*diff(y(x),x)-y(x)=(x-1)*(diff(y(x),x$2)-x+1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 25

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

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