Internal problem ID [2832]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 77.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }+\left (a x +y\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x)+(a*x+y(x))*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 a}{a^{2} x^{2}+2 \RootOf \left (\AiryBi \left (\textit {\_Z} \right ) \left (-2 a^{2}\right )^{\frac {1}{3}} c_{1} x +\left (-2 a^{2}\right )^{\frac {1}{3}} x \AiryAi \left (\textit {\_Z} \right )+2 \AiryBi \left (1, \textit {\_Z}\right ) c_{1}+2 \AiryAi \left (1, \textit {\_Z}\right )\right ) \left (-2 a^{2}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 195
DSolve[y'[x]+(a x+y[x])y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {Ai}'\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \text {Ai}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}{\text {Bi}'\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \text {Bi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}+c_1=0,y(x)\right ] \]