1.19 problem 19

Internal problem ID [7711]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 19
Date solved : Monday, October 21, 2024 at 03:58:16 PM
CAS classification : [`y=_G(x,y')`]

Solve

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

Unknown ode type.

1.19.1 Maple step by step solution

\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & y^{\prime }=\sqrt {1-x^{2}-y^{2}} \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\sqrt {1-x^{2}-y^{2}} \end {array} \]

1.19.2 Maple trace

Methods for first order ODEs:
 

1.19.3 Maple dsolve solution

Solving time : 0.008 (sec)
Leaf size : maple_leaf_size

dsolve(diff(y(x),x) = (1-x^2-y(x)^2)^(1/2), 
       y(x),singsol=all)
 

\[ \text {No solution found} \]

1.19.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

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

Not solved