#### Question

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

#### Solution

The curve passes through point (0, 2).

Therefore, equation (2) becomes:

0 + 2 – 4 = C*e*^{0}

⇒ – 2 = C

⇒ C = – 2

Substituting C = –2 in equation (2), we get:

Is there an error in this question or solution?

Solution Find the Equation of a Curve Passing Through the Point (0, 2) Given that the Sum of the Coordinates of Any Point on the Curve Exceeds the Magnitude of the Slope of the Tangent to the Curve at that Point by 5. Concept: Methods of Solving First Order, First Degree Differential Equations - Linear Differential Equations.