83.3.3 problem 3

Internal problem ID [19059]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:49:43 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

\[ y \left (x \right ) = 1+{\mathrm e}^{\frac {1}{x}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 20

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

\begin{align*} y(x)\to 1+c_1 e^{\frac {1}{x}} \\ y(x)\to 1 \\ \end{align*}