MHT CET20255 May 2025Evening ShiftMathematicsDifferential EquationsActual
The solution of the equation dy d x = 1 x+ y +1 is
Options
- Ax= (x+ y +2)+ c , where c is the constant of integration
- Bx= (x+ y -2)+ c , where c is the constant of integration
- Cy = (x+ y +2)+ c , where c is the constant of integration
- Dy = (x+ y -2)+ c , where c is the constant of integration
Correct answer
C. y = (x+ y +2)+ c , where c is the constant of integration
Step-by-step solution
Substitute z = x + y + 1 , so that dz dx = 1 + dy dx . Substituting into the differential equation dy dx = 1 z yields dz dx - 1 = 1 z which rearranges to dz dx = z + 1 z Separating variables gives z z+1 , dz = dx Integrate both sides: (1 - 1 z+1 ) dz = dx z - |z+1| = x + c Substituting back z = x + y + 1 produces (x + y + 1) - |x + y + 2| = x + c Simplifying, y + 1 - |x + y + 2| = c Rewriting, y = |x + y + 2| + C where C = c - 1 is an arbitrary constant. This matches option C .