MTH421
Question: The D.E : \\ (py^{\’})^{\’}+qy+r\\lambda y=0,\\ a\\leq x\\leq b \\\\ \n \\ c_{1}y(a)+c_{2}y^{\’}(a)=0 \\\\\n \\ c_{3}y(b)+c_{4}y^{\’}(b)=0\\), a corresponding non trivial solution \\ y(x) is called
Answer: eigen function
Question: \\(x^2y^{\’\’}+xy^{\’}-9y=32x^5\\), state the order of the differential equation
Answer: second order
Question: A matrix whose columns are solutions of \\( y^{\’}=A(t)y\\) is called a
Answer: solution matrix
Question: A solution matrix whose columns are linearly independent is called a
Answer: fundamental matrix
Question: The D.E : \\ (py^{\’})^{\’}+qy+r\\lambda y=0,\\ a\\leq x\\leq b \\\\ \n \\ c_{1}y(a)+c_{2}y^{\’}(a)=0 \\\\\n \\ c_{3}y(b)+c_{4}y^{\’}(b)=0\\), a value of the parameter \\lamda for which a non-trivial solution \\ (y\\neq 0 ) exists is called a
Answer: eigen value
Question: \\(x^2y^{\’\’}+xy^{\’}-9y=32x^5\\), what is the class of the problem
Answer: non homogeneous
Question: The D.E : \\ (py^{\’})^{\’}+qy+r\\lambda y=0,\\ a\\leq x\\leq b \\\\ \n \\ c_{1}y(a)+c_{2}y^{\’}(a)=0 \\\\\n \\ c_{3}y(b)+c_{4}y^{\’}(b)=0\\),the differential is called..?
Answer: Sturm Liouville equation
Question: \\(x^2y^{\’\’}+xy^{\’}-9y=32x^5\\), state is structure
Answer: linear
Question: An Operator \\( \\tilde{A}\\) is an extension of A, or A is a restriction of \\( \\tilde{A}\\) if :
Answer: \\ (D(\\tilde{A})\\supset D(A) \\ )and \\( \\tilde{A}x=Ax\\)
Question: A first order ordinary differential equation solved for the derivative has the form :
Answer: \\ (y_{x}^{\’}=f(x,y)\\)
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