Differential Equations — Class 12 Maharashtra HSC Mathematics revision notes
A 4-page visual revision sheet for Differential Equations, written for Class 12 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Differential Equations sheet covers
- Order and Degree
- Order, Degree and Formation
- order: the index of the highest derivative present
- degree: its power, once rationalised to polynomial form
- a family with n arbitrary constants needs n differentiations to remove them all
- differentiate n times, then eliminate the constants between the relation and its derivatives, leaving
- Order and degree, the special cases
- Reading off order and degree
- Forming a differential equation
- Variable Separable Form
- Solving a variable separable equation
- Homogeneous Differential Equations
- Homogeneous equation via y=vx
- Variable separable vs linear
- Variable separable
- Linear, dy/dx+Py=Q
- Linear Differential Equation
- standard form, P and Q functions of x
- integrating factor
- general solution, multiplying through by the I.F.
- Solving a linear differential equation
- Which method actually applies
- Applications: Growth, Decay and Cooling
- Exponential growth from a proportional rate
- Newton's law of cooling
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Differential Equations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.