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Solve the differential equation: dr = a r dθ − θ dr - Mathematics and Statistics

Sum

Solve the differential equation:

dr = a r dθ − θ dr

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Solution

dr = a r dθ − θ dr

∴ (1 + θ) dr = a r dθ

∴ `(dr)/r = a (dθ)/((1 + θ))`

Integrating on both sides, we get

`int (dr)/r = a int (dθ)/(1+θ)`

log | r | = a log | 1 + θ| + log | c |

∴ log | r | = log | c(1 + θ)a|

∴ r = c (1 + θ)a

Concept: Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 4.03 | Page 173
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