CHAPTER 9: DIFFERENTIAL EQUATIONS
Class 12 CBSE Mathematics Core High-Efficiency Formula Sheet
1. Order and Degree Core Checkpoints
• Order: The highest order derivative present in the given differential equation.
• Degree: The power of the highest order derivative when the equation is expressed purely as a
polynomial in its derivatives. Note: If derivatives sit inside functions like sin(dy/dx) or edy/dx, degree is
not defined.
2. Linear Differential Equations Solution Algorithm
Standard profile format: dy/dx + Py = Q (where P and Q are constants or functions of x only).
1. Calculate the structural Integrating Factor (I.F.):
I.F. = e∫P dx
2. Write down the complete general solution equation form:
y · (I.F.) = ∫ (Q · I.F.) dx + C
The Power of 'No': To be a topper, you have to say 'no' to the things that don't matter right now—extra sleep,
mindless scrolling, or hanging out. The result day will prove it was worth it. ego never accepts defeat.
Chapter 9 Notes • Page 1
Class 12 CBSE Mathematics Core High-Efficiency Formula Sheet
1. Order and Degree Core Checkpoints
• Order: The highest order derivative present in the given differential equation.
• Degree: The power of the highest order derivative when the equation is expressed purely as a
polynomial in its derivatives. Note: If derivatives sit inside functions like sin(dy/dx) or edy/dx, degree is
not defined.
2. Linear Differential Equations Solution Algorithm
Standard profile format: dy/dx + Py = Q (where P and Q are constants or functions of x only).
1. Calculate the structural Integrating Factor (I.F.):
I.F. = e∫P dx
2. Write down the complete general solution equation form:
y · (I.F.) = ∫ (Q · I.F.) dx + C
The Power of 'No': To be a topper, you have to say 'no' to the things that don't matter right now—extra sleep,
mindless scrolling, or hanging out. The result day will prove it was worth it. ego never accepts defeat.
Chapter 9 Notes • Page 1
