61.30.27 problem 175

Internal problem ID [12675]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-5
Problem number : 175
Date solved : Tuesday, January 28, 2025 at 03:37:50 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 1413

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

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 3.849 (sec). Leaf size: 85

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

\[ y(x)\to e^{\int \frac {2 a x+b-d x-k}{x (a x+b)+c} \, dx} \left (c_2 \int _1^x\exp \left (\int _1^{K[2]}\frac {-2 b+k+(d-4 a) K[1]}{c+K[1] (b+a K[1])}dK[1]\right )dK[2]+c_1\right ) \]