44.6.28 problem 28

Internal problem ID [7172]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 28
Date solved : Tuesday, February 04, 2025 at 12:43:54 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y y^{\prime }-x&=2 y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 21

dsolve([y(x)*diff(y(x),x)-x=2*y(x)^2,y(1) = 5],y(x), singsol=all)
 

\[ y = \frac {\sqrt {-2+410 \,{\mathrm e}^{4 x -4}-8 x}}{4} \]

✓ Solution by Mathematica

Time used: 3.262 (sec). Leaf size: 39

DSolve[{y[x]*D[y[x],x]-x==2*y[x]^2,{y[1]==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {205 e^{4 x}-e^4 (4 x+1)}}{2 \sqrt {2} e^2} \]