75.6.28 problem 161

Internal problem ID [16784]
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
Date solved : Tuesday, January 28, 2025 at 08:26:12 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }-2 y \,{\mathrm e}^{x}&=2 \sqrt {y \,{\mathrm e}^{x}} \end{align*}

✓ Solution by Maple

Time used: 1.582 (sec). Leaf size: 53

dsolve(diff(y(x),x)-2*y(x)*exp(x)=2*sqrt(y(x)*exp(x)),y(x), singsol=all)
 

\[ \frac {y \,{\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}}-\left (\int {\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}}d x \right ) \sqrt {{\mathrm e}^{x} y}+c_{1} \sqrt {{\mathrm e}^{x} y}}{\sqrt {{\mathrm e}^{x} y}} = 0 \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 56

DSolve[D[y[x],x]-2*y[x]*Exp[x]==2*Sqrt[y[x]*Exp[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2 \left (\sqrt {\pi } \sqrt {y(x)} \text {erf}\left (\frac {\sqrt {e^x y(x)}}{\sqrt {y(x)}}\right )-e^{-e^x} y(x)\right )}{\sqrt {y(x)}}=c_1,y(x)\right ] \]