56.1.68 problem 68

Internal problem ID [8780]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 68
Date solved : Monday, January 27, 2025 at 04:58:27 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} a y y^{\prime \prime }+b y&=c \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 68

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

\begin{align*} a \left (\int _{}^{y}\frac {1}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_{1} a -2 b \textit {\_a} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ -a \left (\int _{}^{y}\frac {1}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_{1} a -2 b \textit {\_a} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.448 (sec). Leaf size: 43

DSolve[a*y[x]*D[y[x],{x,2}]+b*y[x]==c,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2 (c \log (K[1])-b K[1])}{a}}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]