Internal problem ID [2927]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 179.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x +\mathit {a0} +\mathit {a1} x +\left (\mathit {a2} +\mathit {a3} x y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 848
dsolve(x*diff(y(x),x)+a0+a1*x+(a2+a3*x*y(x))*y(x) = 0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.426 (sec). Leaf size: 421
DSolve[x y'[x]+a0+a1 x+(a2+a3 x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \left (\sqrt {\text {a1}} c_1 \text {HypergeometricU}\left (\frac {1}{2} \left (\text {a2}+\frac {i \text {a0} \sqrt {\text {a3}}}{\sqrt {\text {a1}}}\right ),\text {a2},2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )+c_1 \left (\sqrt {\text {a1}} \text {a2}+i \text {a0} \sqrt {\text {a3}}\right ) \text {HypergeometricU}\left (\frac {1}{2} \left (\frac {i \text {a0} \sqrt {\text {a3}}}{\sqrt {\text {a1}}}+\text {a2}+2\right ),\text {a2}+1,2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )+\sqrt {\text {a1}} \left (2 \text {LaguerreL}\left (-\frac {i \text {a0} \sqrt {\text {a3}}}{2 \sqrt {\text {a1}}}-\frac {\text {a2}}{2}-1,\text {a2},2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )+\text {LaguerreL}\left (-\frac {\text {a2}}{2}-\frac {i \text {a0} \sqrt {\text {a3}}}{2 \sqrt {\text {a1}}},\text {a2}-1,2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )\right )\right )}{\sqrt {\text {a3}} \left (c_1 \text {HypergeometricU}\left (\frac {1}{2} \left (\text {a2}+\frac {i \text {a0} \sqrt {\text {a3}}}{\sqrt {\text {a1}}}\right ),\text {a2},2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )+\text {LaguerreL}\left (-\frac {\text {a2}}{2}-\frac {i \text {a0} \sqrt {\text {a3}}}{2 \sqrt {\text {a1}}},\text {a2}-1,2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )\right )} \\ y(x)\to \frac {\frac {\left (\text {a0} \sqrt {\text {a3}}-i \sqrt {\text {a1}} \text {a2}\right ) \text {HypergeometricU}\left (\frac {1}{2} \left (\frac {i \text {a0} \sqrt {\text {a3}}}{\sqrt {\text {a1}}}+\text {a2}+2\right ),\text {a2}+1,2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )}{\text {HypergeometricU}\left (\frac {1}{2} \left (\text {a2}+\frac {i \text {a0} \sqrt {\text {a3}}}{\sqrt {\text {a1}}}\right ),\text {a2},2 i \sqrt {\text {a1}} \sqrt {\text {a3}} x\right )}-i \sqrt {\text {a1}}}{\sqrt {\text {a3}}} \\ \end{align*}