Question
The solution of the differential equation
with
exists, but is not unique.
Answer :
Word Count : 92
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The differential equation [ \frac{dy}{dx}=y ] is separable. Writing [ \frac{1}{y},dy=dx ] and integrating, [ \ln|y|=x+C. ] Hence [ y=Ce^{x}. ]
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Related Questions
Solve: .
मान लीजिए एक थर्मामीटर जिसके घर के अंदर रीडिंग है, उसे बाहर रखा जाता है, जहाँ वायु तापमान
है। दो मिनट के बाद थर्मामीटर की रीडिंग
पाई जाती है। किसी भी समय t पर थर्मामीटर के तापमान की रीडिंग T(t) ज्ञात कीजिए।
State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example:
a) y2 is an integrating factor of the differential equation:
.
) Solve the equation .
प्राचल विचरण विधि से निम्नलिखित अवकल समीकरण: को हल कीजिए।
Using Charpit's method, solve the equation
Solve: .