38.5.63 problem 53

Internal problem ID [8411]
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, September 30, 2025 at 05:35:54 PM
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*}

✓ Maple. Time used: 0.188 (sec). Leaf size: 20

ode:=diff(y(x),x) = exp(x^(1/2))/y(x); 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \sqrt {2} \sqrt {\int _1^xe^{\sqrt {K[1]}}dK[1]+8} \end{align*}

✓ Sympy. Time used: 0.355 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(sqrt(x))/y(x),0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {4 \sqrt {x} e^{\sqrt {x}} - 4 e^{\sqrt {x}} + 16} \]