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

**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.

To solve the given differential equation, we make the substitution
3*x* + *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

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