Definitions [1]
Definition: Equations Reducible to Linear Equations
A pair of equations that is not linear in the original variables xxx and yyy, but becomes a pair of linear equations after a suitable substitution, is called a pair of equations reducible to linear equations.
Key Points
Key Points: Equations Reducible to Linear Equations
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Some equations are not linear in the given variables.
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By a suitable change of variables, they can be reduced to linear equations.
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After substitution, the equations become linear in the new variables.
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Denominators must not be zero.
Important Questions [9]
- Prove that for an Astroid X 2 3 + Y 2 3 = a 2 3 the Line 𝜽=𝝅/𝟔 Divide the Arc in the First Quadrant in a Ratio 1:3.
- Solve : ( 1 + Log X . Y ) D X + ( 1 + X Y ) Dy=0
- Evaluate ∫ 1 0 X 5 Sin − 1 X D X and Find the Value of β ( 9 2 , 1 2 )
- Solve the Ode ( Y + 1 3 Y 3 + 1 2 X 2 ) D X + ( X + X Y 2 ) D Y = 0
- Evaluate ∫ ∞ 0 5 − 4 X 2 D X
- Solve Y D X + X ( 1 − 3 X 2 Y 2 ) D Y = 0
- Solve ( Y − X Y 2 ) D X − ( X + X 2 Y ) D Y = 0
- Solve X 2 D 2 Y D X 2 + 3 X D Y D X + 3 Y = Log X . Cos ( Log X ) X
- Evaluate ∫ 6 0 d x 1 + 3 x by using 1} Trapezoidal 2} Simpsons (1/3) rd. and 3} Simpsons (3/8) Th rule.
Concepts [4]
- Exact Differential Equations
- Equations Reducible to Exact Form by Using Integrating Factors
- Equations Reducible to Linear Equations
- Simple Application of Differential Equation of First Order and First Degree to Electrical and Mechanical Engineering Problem
