Internal problem ID [15054]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 161.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-2 y \,{\mathrm e}^{x}-2 \sqrt {y \,{\mathrm e}^{x}}=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 53
dsolve(diff(y(x),x)-2*y(x)*exp(x)=2*sqrt(y(x)*exp(x)),y(x), singsol=all)
\[ \frac {y \left (x \right ) {\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}}-\left (\int {\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}}d x \right ) \sqrt {y \left (x \right ) {\mathrm e}^{x}}+c_{1} \sqrt {y \left (x \right ) {\mathrm e}^{x}}}{\sqrt {y \left (x \right ) {\mathrm e}^{x}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 56
DSolve[y'[x]-2*y[x]*Exp[x]==2*Sqrt[y[x]*Exp[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \left (\sqrt {\pi } \sqrt {y(x)} \text {erf}\left (\frac {\sqrt {e^x y(x)}}{\sqrt {y(x)}}\right )-e^{-e^x} y(x)\right )}{\sqrt {y(x)}}=c_1,y(x)\right ] \]