Ex 9.3, 4 - Chapter 9 Class 12 Differential Equations

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Ex 9.3, 4 Form a differential equation representing the given family of curves by eliminating arbitrary constants and . = 2 + = 2 + Differentiating Both Sides w.r.t. = 2 + = 2 . + + 2 + = 2 2 + + 2 . = + + Again differentiating w.r.t.x ^ = / ( ^2 [2 +2 + ]) y = ( ( ^2 ))/ [2 +2 + ]+ ^2 ( [2 +2 + ])/ y = 2 ^2 [2 +2 + ]+ ^2 2 Putting y = ^2 [2 +2 + ] y = 2y + ^2 2 y = 2y + 2 ^2 y 2y = 2 ^2 Also, y 2y = ^2 [2 +2 + ] 2 ^2 ( + ) y 2y = 2a ^2 +2 ^2 + ^2 2 ^2 2 ^2 y 2y = (2 ^2 2 ^2 )+(2 ^2 2 ^2 )+ ^2 y 2y = 0 + 0 + ^2 y 2y = ^2 Now ((1))/((2)) , ( " 2 )/( ^( ) 2 )=(2 ^2 )/( ^2 ) ( ^ 2 ^ )/( ^ 2 )= 2 y 2y = 2(y 2y) y 2y = 2y 4y y 2y 2y 4y = 0 y 4y 4y = 0