44.6.49 problem 49

Internal problem ID [7193]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 49
Date solved : Tuesday, February 04, 2025 at 12:46:28 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} 1&=\left (y^{2}+x \right ) y^{\prime } \end{align*}

✓ Solution by Maple

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

dsolve(1=(x+y(x)^2)*diff(y(x),x),y(x), singsol=all)
 

\[ x +y^{2}+2 y+2-{\mathrm e}^{y} c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 24

DSolve[1==(x+y[x]^2)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=-y(x)^2-2 y(x)+c_1 e^{y(x)}-2,y(x)\right ] \]