61.24.74 problem 74
Internal
problem
ID
[12487]
Book
:
Handbook
of
exact
solutions
for
ordinary
differential
equations.
By
Polyanin
and
Zaitsev.
Second
edition
Section
:
Chapter
1,
section
1.3.
Abel
Equations
of
the
Second
Kind.
subsection
1.3.3-2.
Problem
number
:
74
Date
solved
:
Tuesday, January 28, 2025 at 08:01:45 PM
CAS
classification
:
[[_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime } y+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \end{align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 307
dsolve(y(x)*diff(y(x),x)+a*(1+2*b*x^(1/2))*exp(2*b*x^(1/2))*y(x)=-a^2*b*x^(3/2)*exp(4*b*x^(1/2)),y(x), singsol=all)
\[
\frac {\sqrt {x}\, \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\, \operatorname {BesselI}\left (1, \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right ) c_{1} b -\operatorname {BesselK}\left (1, -\sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right ) \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\, b \sqrt {x}-\operatorname {BesselI}\left (0, \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right ) c_{1} +\operatorname {BesselK}\left (0, -\sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right )}{\operatorname {BesselI}\left (1, \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right ) \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\, b \sqrt {x}-\operatorname {BesselI}\left (0, \sqrt {\frac {a \,{\mathrm e}^{2 b \sqrt {x}}}{b^{2} \left ({\mathrm e}^{2 b \sqrt {x}} a x +y\right )}}\right )} = 0
\]
✗ Solution by Mathematica
Time used: 0.000 (sec). Leaf size: 0
DSolve[y[x]*D[y[x],x]+a*(1+2*b*x^(1/2))*Exp[2*b*x^(1/2)]*y[x]==-a^2*b*x^(3/2)*exp(4*b*x^(1/2)),y[x],x,IncludeSingularSolutions -> True]
Not solved