Examples

Chapter 9 Class 12 Differential Equations
Serial order wise

### Transcript

Example 20 Find the particular solution of the differential equation log(šš¦/šš„)=3š„+4š¦ given that š¦=0 š¤āšš š„=0 log(šš¦/šš„)=3š„+4š¦ šš/šš = e(3x + 4y) šš¦/šš„ = e3x e4y Separating the variables šš¦/š^4š¦ = e3x dx eā4y dy = e3x dx Integrating both sides ā«1āćš^(ā4š¦) šš¦ć=ā«1āš^3š„ šš„ š^(āšš)/(āš)=š^šš/š+šŖ 0=š^3š„/3+š^(ā4š¦)/4+š¶ š^3š„/3 + š^(ā4š¦)/4 + C = 0 (4š3š„" + " 3š^(ā4š¦))/12 + C = 0 (4š3š„" + " 3š^(ā4š¦) + 12š¶)/12 " = 0" šš^šš + šš^(āšš) + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4š^(3(0)) + 3š^(ā4(0)) + 12C = 0 4š^0 + 3š^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = ā 7 C = (āš)/šš Putting value of C in (1) 4š^3š„ + 3š^(ā4š¦) + 12C = 0 4š^3š„ + 3š^(ā4š¦) + 12((ā7)/12) = 0 šš^šš + šš^(āšš) ā 7 = 0