77.1.118 problem 145 (page 213)

Internal problem ID [18008]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 145 (page 213)
Date solved : Tuesday, January 28, 2025 at 11:19:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve((2*x+1)*diff(y(x),x$2)+(4*x-2)*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = 4 c_{1} x^{2}+c_{2} {\mathrm e}^{-2 x}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 27

DSolve[(2*x+1)*D[y[x],{x,2}]+(4*x-2)*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} c_2 \left (4 x^2+1\right )+c_1 e^{-2 x} \]