Internal problem ID [8425]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 88.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {2 y^{\prime }-3 y^{2}-4 a y=b +c \,{\mathrm e}^{-2 a x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 420
dsolve(2*diff(y(x),x) - 3*y(x)^2 - 4*a*y(x) - b - c*exp(-2*a*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {\sqrt {3}\, \sqrt {c}\, c_{1} \operatorname {BesselY}\left (-\frac {\sqrt {4 a^{2}-3 b}-2 a}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )}{3 \left (\operatorname {BesselY}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right ) c_{1} +\operatorname {BesselJ}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )\right )}-\frac {\operatorname {BesselJ}\left (-\frac {\sqrt {4 a^{2}-3 b}-2 a}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right ) \sqrt {3}\, \sqrt {c}}{3 \left (\operatorname {BesselY}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right ) c_{1} +\operatorname {BesselJ}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )\right )}\right ) {\mathrm e}^{-a x}-\frac {\left (\sqrt {4 a^{2}-3 b}\, c_{1} +2 c_{1} a \right ) \operatorname {BesselY}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )+\left (\sqrt {4 a^{2}-3 b}+2 a \right ) \operatorname {BesselJ}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )}{3 \left (\operatorname {BesselY}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right ) c_{1} +\operatorname {BesselJ}\left (-\frac {\sqrt {4 a^{2}-3 b}}{2 a}, \frac {\sqrt {3}\, \sqrt {c}\, {\mathrm e}^{-a x}}{2 a}\right )\right )} \]
✓ Solution by Mathematica
Time used: 2.009 (sec). Leaf size: 2746
DSolve[2*y'[x] - 3*y[x]^2 - 4*a*y[x] - b - c*Exp[-2*a*x]==0,y[x],x,IncludeSingularSolutions -> True]
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