76.3.15 problem 15

Internal problem ID [17386]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 10:04:02 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {4 t}{y} \end{align*}

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(t),t)=-4*t/y(t),y(0) = y__0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 37

DSolve[{D[y[t],t]==-4*t/y[t],{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt {\text {y0}^2-4 t^2} \\ y(t)\to \sqrt {\text {y0}^2-4 t^2} \\ \end{align*}