57.1.23 problem 23

Internal problem ID [9007]
Book : First order enumerated odes
Section : section 1
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:27:06 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{y} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 69

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

\begin{align*} y &= -\frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 a x b -2 a c}}{2 b} \\ y &= \frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 a x b -2 a c}}{2 b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.918 (sec). Leaf size: 85

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

\begin{align*} y(x)\to -\frac {i \sqrt {a b x+\frac {a c}{2}+b^2 c_1 \left (-e^{\frac {2 b x}{c}}\right )}}{b} \\ y(x)\to \frac {i \sqrt {a b x+\frac {a c}{2}+b^2 c_1 \left (-e^{\frac {2 b x}{c}}\right )}}{b} \\ \end{align*}