72.1.35 problem 38

Internal problem ID [14635]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 06:45:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {y^{2}+5}{y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.094 (sec). Leaf size: 16

dsolve([diff(y(t),t)=(y(t)^2+5)/y(t),y(0) = -2],y(t), singsol=all)
 

\[ y = -\sqrt {9 \,{\mathrm e}^{2 t}-5} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 20

DSolve[{D[y[t],t]==(y[t]^2+5)/y[t],{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\sqrt {9 e^{2 t}-5} \]