MHT CET202410 May 2024Evening ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation e ^ y-x ~d y ~d x =y ( x+ x 1+y y ) . is
Options
- Ae ^y y= e ^x x+ c , where c is a constant of integration.
- Be ^y= e ^x x+ c , where c is a constant of integration.
- Cy= e ^x x+ c , where c is a constant of integration.
- Dy y= e ^x x+ c , where c is a constant of integration.
Correct answer
A. e ^y y= e ^x x+ c , where c is a constant of integration.
Step-by-step solution
array ll & e ^ y-x ~d y ~d x =y ( x+ x 1+y y ) & e ^y e ^x ~d y ~d x = y (1+y y) ( x+ x) & e ^y (1+y y) y ~d y= e ^x( x+ x) d x & e ^y ( y+ 1 y ) d y= e ^x( x+ x) d x array Integrating both sides, we get aligned & e ^y y= e ^x x+ c & [ e ^x [ f (x)+ f ^ (x) ] d x= e ^x f (x)+ c ] aligned