44.5.35 problem 35

Internal problem ID [7097]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:57:31 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1+3 x}{2 y} \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 18

dsolve([diff(y(x),x)=(3*x+1)/(2*y(x)),y(-2) = -1],y(x), singsol=all)
 

\[ y = -\frac {\sqrt {6 x^{2}+4 x -12}}{2} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 21

DSolve[{D[y[x],x]==(3*x+1)/(2*y[x]),{y[-2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {\frac {3 x^2}{2}+x-3} \]