Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

NCERT Solutions for Class 12 Maths Chapter 9 - Image 225

Since, the curve passes through origin.

Thus, equation 2 becomes

1 = C

Substituting C = 1 in equation 2, we get,

    \[x\text{ }+\text{ }y\text{ }+\text{ }1\text{ }=\text{ }{{e}^{x}}\]

Therefore, the required general solution of the given differential equation is

    \[x\text{ }+\text{ }y\text{ }+\text{ }1\text{ }=\text{ }{{e}^{x}}\]