Find the deflection of the fixed end vibrating string of unit length corresponding to zero initial deflection and ) u(x given below as the initial velocity.
The problem requires finding the deflection \( y(x,t) \) of a vibrating string of unit length, fixed at both ends, with zero initial deflection and a given initial velocity \( u(x) \). The wave equation governing the motion is: \[ \frac{\partial^2 y}{\partial t^2} = c^2 \frac{\partial^2 y}{\partial x^2} \] where \( c ____ ___ ________ ______ ________ _______ ________ _________ ___ ____ _________ ______.
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रैखिक आंशिक अवकल समीकरण x(y2 + z)p-y(x2 + z)q = (x2- y2) z का वह समाकल पृष्ठ ज्ञात कीजिए जिसमें सरल रेखा x + y = 0, z = 1 आविष्ट हो।
Solve the differential equation
where
अवकल समीकरण का व्यापक हल प्राप्त कीजिए।
दिखाइए कि अवकल समीकरण
के लिए emx विशेष समाकल है यदि m² + am+b = 0. अतः m का वह मान ज्ञात कीजिए जिसके लिए exm समीकरण
का एक विशेष समाकल हो।
Using Jacobi’s method find the complete integral of the equation
समीकरण y" + w²y = 0 के संगत रिकेटी समीकरण ज्ञात कीजिए।
A mass m , free to move along a line is attracted towards a given point on the line with a force proportional to its distance from the given point. If the mass starts from rest at a distance x0 from the given point, show that the mass moves in a simple harmonic motion.