Exercise 4.3 Class 12 Math Solutions - Unit 4 Differential Equations, Punjab Board
Step-by-step solutions to Exercise 4.3, Unit 4: Differential Equations, for Class 12 Punjab Board students. Covers practical real-world applications of first-order differential equations across population growth, radioactive decay, economic deflation, Newton's law of cooling, and series RL electrical circuits, worked out question by question.
Exercise Overview
Exercise 4.3 concludes Unit 4: Differential Equations in Class 12 Mathematics under the Punjab Board PCTB / PECTAA curriculum by demonstrating the widespread utility of First-Order ODEs across physics, biology, economics, and electrical engineering. In natural sciences, the exercise solves exponential growth and decay models where the rate of change is proportional to the current quantity ((\frac{dy}{dt} = ky)), yielding closed-form exponential solutions (y(t) = y_0 e^{kt}) for calculating bacterial doubling intervals and isotopic half-life decay periods.
In thermodynamics and economics, students apply differential equations to thermal dissipation via Newton's Law of Cooling (\frac{dT}{dt} = -k(T - T_m)), calculating cooling rates and equilibrium temperatures, as well as economic capital and price deflation trends. In electrical engineering, the exercise investigates transient current growth in series RL circuits governed by (L\frac{di}{dt} + Ri = E(t)), determining the time constant (\tau = \frac{L}{R}) and steady-state saturation currents.
For Punjab Board HSSC Part 2 examinations across all nine educational divisions (Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, Bahawalpur, Sargodha, Sahiwal, and D.G. Khan), Exercise 4.3 is a primary source of high-yield applied word problems in Section C Long Questions. These step-by-step solutions provide clean initial value setups, clear exponential integrations, and complete numerical evaluations for every problem.