Internal problem ID [3547]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 816.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.087 (sec). Leaf size: 71
dsolve(diff(y(x),x)^2+(a+6*y(x))*diff(y(x),x)+y(x)*(3*a+b+9*y(x)) = 0,y(x), singsol=all)
\begin{align*} x -\left (\int _{}^{y \relax (x )}\frac {1}{-\frac {a}{2}-3 \textit {\_a} -\frac {\sqrt {-4 b \textit {\_a} +a^{2}}}{2}}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{-\frac {a}{2}-3 \textit {\_a} +\frac {\sqrt {-4 b \textit {\_a} +a^{2}}}{2}}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.613 (sec). Leaf size: 175
DSolve[(y'[x])^2+(a+6 y[x])y'[x]+y[x](3 a+b+9 y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {(3 a+2 b) \log \left (-3 \sqrt {a^2-4 \text {$\#$1} b}+3 a+2 b\right )+3 a \log \left (\sqrt {a^2-4 \text {$\#$1} b}+a\right )}{6 (3 a+b)}\&\right ]\left [-\frac {x}{2}+c_1\right ] \\ y(x)\to \text {InverseFunction}\left [-\frac {3 a \log \left (a-\sqrt {a^2-4 \text {$\#$1} b}\right )+(3 a+2 b) \log \left (3 \sqrt {a^2-4 \text {$\#$1} b}+3 a+2 b\right )}{6 (3 a+b)}\&\right ]\left [\frac {x}{2}+c_1\right ] \\ y(x)\to 0 \\ y(x)\to \frac {1}{9} (-3 a-b) \\ \end{align*}