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# Substitution Method

Solution of First Order and First Degree Differential Equations: Substitution Method

## Solution of First Order and First Degree Differential Equations

Substitution Method

Let the differential equation be of the form dy/dx = f (ax + by + c).

(i) If a ≠ 0 and b ≠ 0 , then the substitution ax + by + c = z reduces the given equation to the variables separable form.

(ii) If a = 0 or b = 0 , then the differential equation is already in separable form.   ### Example 10.16 ### Solution

To solve the given differential equation, we make the substitution 3x + y + 4 = z.

Differentiating with respect to x, we get dy/dx = dz/dx − 3 . So the given differential equation becomes In this equation variables are separable. So, separating the variables and integrating, we get the general solution of the given differential equation as Tags : Solution of First Order and First Degree Differential Equations | Mathematics , 12th Maths : UNIT 10 : Ordinary Differential Equations
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12th Maths : UNIT 10 : Ordinary Differential Equations : Substitution Method | Solution of First Order and First Degree Differential Equations | Mathematics