83.27.12 problem 12

Internal problem ID [19358]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:35:22 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve((a*x-b*x^2)*diff(y(x),x$2)+2*a*diff(y(x),x)+2*b*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} +\left (-b x +a \right )^{3} c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 32

DSolve[(a*x-b*x^2)*D[y[x],{x,2}]+2*a*D[y[x],x]+2*b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\frac {c_2 (b x-a)^3}{b}+3 c_1}{3 x} \]