Internal problem ID [4055]
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]
\[ \boxed {{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 309
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*} y \left (x \right ) = -\frac {\operatorname {RootOf}\left (3 \ln \left (-\frac {4 b}{\left (3 \textit {\_Z} -2 b \right )^{2}}\right ) a +2 \ln \left (-\frac {4 b}{\left (3 \textit {\_Z} -2 b \right )^{2}}\right ) b -3 a \ln \left (-\frac {\left (\textit {\_Z} +2 a \right )^{2}}{4 b}\right )+18 a c_{1} +6 c_{1} b -18 a x -6 x b \right ) \left (\operatorname {RootOf}\left (3 \ln \left (-\frac {4 b}{\left (3 \textit {\_Z} -2 b \right )^{2}}\right ) a +2 \ln \left (-\frac {4 b}{\left (3 \textit {\_Z} -2 b \right )^{2}}\right ) b -3 a \ln \left (-\frac {\left (\textit {\_Z} +2 a \right )^{2}}{4 b}\right )+18 a c_{1} +6 c_{1} b -18 a x -6 x b \right )+2 a \right )}{4 b} y \left (x \right ) = -\frac {{\mathrm e}^{\operatorname {RootOf}\left (-3 a \ln \left (-\frac {1}{4 b}\right )-3 \ln \left (-\frac {\left (3 \,{\mathrm e}^{\textit {\_Z}}+6 a +2 b \right )^{2}}{4 b}\right ) a -2 \ln \left (-\frac {\left (3 \,{\mathrm e}^{\textit {\_Z}}+6 a +2 b \right )^{2}}{4 b}\right ) b +18 a c_{1} +6 c_{1} b -6 a \textit {\_Z} -18 a x -6 x b \right )} \left ({\mathrm e}^{\operatorname {RootOf}\left (-3 a \ln \left (-\frac {1}{4 b}\right )-3 \ln \left (-\frac {\left (3 \,{\mathrm e}^{\textit {\_Z}}+6 a +2 b \right )^{2}}{4 b}\right ) a -2 \ln \left (-\frac {\left (3 \,{\mathrm e}^{\textit {\_Z}}+6 a +2 b \right )^{2}}{4 b}\right ) b +18 a c_{1} +6 c_{1} b -6 a \textit {\_Z} -18 a x -6 x b \right )}+2 a \right )}{4 b} \end{align*}
✓ Solution by Mathematica
Time used: 0.634 (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*}