Learning these TS Inter 2nd Year Maths 2B Formulas Chapter 8 Differential Equations will help students to solve mathematical problems quickly.

## TS Inter 2nd Year Maths 2B Differential Equations Formulas

→ An equation involving one dependent variable and its derivatives with respect to one or more independent variables is called a differential equation. If the equation contains only one independent variable then it is called an ordinary differential equation and if it contains more than one independent variable then it is called a partial differential equation,

→ If the differential equation is of the form f(x) dx + g(y)dy = 0 then its solution is ∫ f(x) dx + ∫ g(y) dy = 0.

→ The order of a differential equation is the order of the highest derivative occurring in it and the largest exponent of the highest order derivative in the equation is called the degree of the differential equation.

→ By eliminating the arbitrary constants in the given equation, we can formulate the differential equation.

→ If the differential equation is of the form \(\frac{d y}{d x}=\frac{f(x, y)}{g(x, y)}\), where f and g are homogeneous functions of x and y of same degree, then we put y = vx and obtain the form Φ(υ) dυ = \(\frac{d x}{x}\) and on integration gives the solution.

→ If the differential equation is of the form

\(\frac{d y}{d x}=\frac{a x+b y+c}{a^{\prime} x+b^{\prime} y+c^{\prime}}\), where a, b, c, a, b, c are constants.

- If b = – a’ then its solution can be obtained by term by term integration after regrouping.
- If \(\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}\) = m then we put ax + by = v and bring it in the form Φ(υ) dυ = \(\frac{d x}{x}\) and then integrate.
- If \(\frac{a}{a^{\prime}} \neq \frac{b}{b^{\prime}}\), then put x = X + h, y = Y + k (h, k are obtained by solving ah + bk + c = 0 and

a’h + b’k + c’ = 0 and bring it to the form \(\)

Then take Y = VX and obtain Φ(V) dV = \(\frac{d X}{X}\) and then integrate.

→ If the differential equation is of the form \(\frac{d y}{d x}\) + Py = Q then the solution is

ye_{∫pdx} = C + ∫Q_{e∫pdx}dx.