सत्यापित कीजिए कि अवकल समीकरण :
z(x2-y2-z²)dx+(x+z)xzdy +x(z²-x2-xy)dz = 0
समाकलनीय है और इसका समाकल भी ज्ञात कीजिए।
दिए गए अवकल समीकरण को हल करने के लिए, पहले इसे निम्नलिखित रूप में लिखा जाता है: \[ P dx + Q dy + R dz = 0 \] जहाँ ________ ___ _________ ____ ______ ________ __________ _________ __________ _________.
________ _____ _______ _______ _______ _______ ______ __________.
___ _______ __________ _____ _____ ____ ____ ________ _____ _________ _____.
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______ __________ _____ _______ _________ ________.
_____ ____ __________ _____ _________ ___.
________ _________ ___ _____ _________ ______ _____ ___ ___ _________.
____ _________ _____ _________ _________.
________ _____ ____ _____ _______ ______ _______ ________.
____ _________ _____ ____ _______ _____ ________.
_______ ___ _________ ___ _________ _________ ________ _____ __________ ______ _______ _______.
____ ____ ___ _____ _______ ___ __________ _________ __________ _______.
______ __________ __________ ____ ________.
________ ________ _______ _____ ________ _____ _____ _____ ________ ___ ________.
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State Euler’s theorem for homogeneous functions and verify it for the function:
By using the method of variation of parameter, find the general solution of the differential equation:
b) If:
Z= x²y+2xy²
where x = sin zt
and
y = cost
find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.
If:
Z= x²y+2xy²
where x = sin zt
and
y = cost
find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.
Show that the following function is not continuous at (0,0):
Solve the differential equations:
समीकरण :
x(y²-z²)ux + y(z² -x²)u, +z(x²-y²)u₂ = 0
समघात फलनों के लिए, ऑयलर प्रमेय का कथन लिखिए तथा फलन के लिए उसका सत्यापन कीजिए।