78.1.40 problem 4 (b)

Internal problem ID [18095]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (b)
Date solved : Tuesday, January 28, 2025 at 11:26:08 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 10

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

\[ y = x^{2}+\ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 11

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

\[ y(x)\to x^2+\log (x) \]