44.5.63 problem 53

Internal problem ID [7125]
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 : 53
Date solved : Tuesday, February 04, 2025 at 12:23:07 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.153 (sec). Leaf size: 20

dsolve([diff(y(x),x)=exp(sqrt(x))/y(x),y(1) = 4],y(x), singsol=all)
 

\[ y = 2 \sqrt {4+{\mathrm e}^{\sqrt {x}} \left (\sqrt {x}-1\right )} \]

✓ Solution by Mathematica

Time used: 1.907 (sec). Leaf size: 28

DSolve[{D[y[x],x]==Exp[Sqrt[x]]/y[x],{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

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